This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
Seismic inversion is a process of extracting information about the subsurface from data measured at the surface of the Earth during a seismic acquisition survey. In a typical seismic survey, seismic waves are generated by a source 101 positioned at a desired location. As the source generated waves propagate through the subsurface, some of the energy reflects from subsurface interfaces 105, 107, and 109 and travels back to the surface 111, where it is recorded by the receivers 103. The seismic waves 113 and 115 that have been reflected in the subsurface only once before reaching the recording devices are called primary reflections. In contrast, multiple reflections 117 and 119 are the seismic waves that have reflected multiple times along their travel path back to the surface (dashed lines in FIG. 1). Surface-related multiple reflections are the waves that have reflected multiple times and incorporate the surface of the Earth or the water surface in their travel path before being recorded.
As illustrated by FIG. 2, the generation of surface-related multiples requires that a free surface boundary condition be imposed. FIG. 2 illustrates interbed multiple 202 and free surface multiple 204. As discussed later in the detailed description section, the present technological advancement can remove free surface multiples from a data set. The dashed component 206 of the free surface multiple would not occur in the presence of an absorbing boundary condition.
Most seismic inversion methods rely on primary reflections only and treat all other seismic modes, including multiple reflections as “noise” that need to be suppressed during conventional seismic data processing prior to inversion. There are a number of multiple suppression methods available in industry. For example, suppression methods include surface-related multiple elimination (SRME), shallow water demultiple (SWD), model-based water-layer demultiple (MWD), and predictive deconvolution. Those of ordinary skill in the art are familiar with these suppression methods, and further discussion is not needed. However, all of the methods struggle with multiple elimination if the multiple and primary reflections overlap in the recorded seismic data. Furthermore, inadequate application of multiple suppression methods may result in damage to the primary data, rendering it unusable for inversion.
An alternative approach is to use inversion algorithms which accept the data that still contain surface-related multiples. Full Wavefield Inversion (FWI) is a seismic method capable of utilizing the full seismic record, including the seismic events that are treated as “noise” by standard inversion algorithms. The goal of FWI is to build a realistic subsurface model by minimizing the misfit between the recorded seismic data and synthetic (or modeled) data obtained via numerical simulation.
FWI is a computer-implemented geophysical method that is used to invert for subsurface properties such as velocity or acoustic impedance. The crux of any FWI algorithm can be described as follows: using a starting subsurface physical property model, synthetic seismic data are generated, i.e. modeled or simulated, by solving the wave equation using a numerical scheme (e.g., finite-difference, finite-element etc.). The term velocity model or physical property model as used herein refers to an array of numbers, typically a 3-D array, where each number, which may be called a model parameter, is a value of velocity or another physical property in a cell, where a subsurface region has been conceptually divided into discrete cells for computational purposes. The synthetic seismic data are compared with the field seismic data and using the difference between the two, an error or objective function is calculated. Using the objective function, a modified subsurface model is generated which is used to simulate a new set of synthetic seismic data. This new set of synthetic seismic data is compared with the field data to generate a new objective function. This process is repeated until the objective function is satisfactorily minimized and the final subsurface model is generated. A global or local optimization method is used to minimize the objective function and to update the subsurface model.
Numerical simulation can generate data with or without free surface multiples depending on the boundary condition imposed on top of the subsurface model. The free surface boundary condition yields data with surface-related multiples, while the transparent (absorbing) boundary condition allows for generation of multiple-free data. These two modes of numerical modeling lead to two standard approaches in FWI.
In one approach, FWI requires that the input seismic data have undergone some kind of multiple suppression procedure and uses absorbing boundary condition to model multiple-free synthetic data. In the other approach, the data still contain surface-related multiples which have to be modeled by imposing a free-surface boundary condition. The second approach is preferable, since it saves both time and resources required by application of conventional multiple suppression methods. Furthermore, it ensures that the integrity of the data is not compromised and has the potential of extracting additional information contained in multiple reflections. The drawback of the second approach is that it requires accurate modeling of surface-related multiples, which appear to be extremely sensitive to errors in the water-bottom reflectivity, source signature, location, etc. Even a small mismatch between the measured and simulated multiples may result in FWI models that are contaminated by the multiples of strong-contrast interfaces.
U.S. Pat. No. 7,974,824, the entire contents of which are hereby incorporated by reference, describes the seismic inversion of data containing surface-related multiples. Instead of pre-processing seismic data to remove surface-related multiples, a seismic waveform inversion process enables comparison of simulated seismic data containing surface-related multiples with observed seismic data also containing surface-related multiples. Based on this comparing, a model of a subterranean structure can be iteratively updated.
Zhang and Schuster (2013) describes a method where least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. Zhang D. and Schuster G., “Least-squares reverse time migration of multiples,” Geophysics, Vol. 79, S11-S21, 2013.